The implied volatility smirk

Jin Zhang and Yi Xiang

Quantitative Finance, 2008, vol. 8, issue 3, 263-284

Abstract: This paper provides an industry standard on how to quantify the shape of the implied volatility smirk in the equity index options market. Our local expansion method uses a second-order polynomial to describe the implied volatility-moneyness function and relates the coefficients of the polynomial to the properties of the implied risk-neutral distribution of the equity index return. We present a formal, two-way representation of the link between the level, slope and curvature of the implied volatility smirk and the risk-neutral standard deviation, skewness and excess kurtosis. We then propose a new semi-analytical method to calibrate option-pricing models based on the quantified implied volatility smirk, and investigate the applicability of two option-pricing models.

Keywords: Option pricing; Implied volatility smirk; Risk-neutral skewness and excess kurtosis; Term structure (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (34)

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DOI: 10.1080/14697680601173444

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